We can solve y=(2+4x^2)^3 in two ways. One is use the chain rule

y=(2+4x^2)^3

y' = 3*8x*(2 + 4x^2)^2

=> y' = 24x*( 4 + 16x^4 + 16x^2)

=> y' = 96x + 384x^5 + 384x^3

Else expand (2+4x^2)^3

y=(2+4x^2)^3

=> 8 + 64x^6 + 96x^4 + 48x^2

y' = 384x^5 + 384x^3 + 96x

**The derivative of y=(2+4x^2)^3 is 384x^5 + 384x^3 + 96x**